This Week (3) Concepts: Light and Earth’s Energy Balance Electromagnetic Radiation Blackbody Radiation and Temperature Earth’s Energy Balance w/out atmosphere Read chapter 3 (34 – 41.5) of your text Keep up by working on assignment 1

Today—Light What is light? How much energy does light have? Emission and Absorption Spectra

Oscillators -+

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- + As charged particles oscillate, their motion causes the electric force field to oscillate. Oscillations in the electric and magnetic fields (caused by one another) can propagate (move) through space. Such oscillations are known as electromagnetic radiation (which encompasses light)

Electromagnetic Radiation Electric and magnetic fields oscillate perpendicular to each other and to direction of propagation (travel). Wavelength ( ): distance between peaks (1 full cycle)—m,cm,nm Frequency ( ): # of full cycles passing a point per second – Hz and related to each other by speed of light (c): = c/

Electromagnetic Radiation Light acts both like a wave and as a stream of particles We call these packets of light photons A photon is the smallest packet of energy that can be transported by an EM wave of a given frequency. The energy a photon carries is directly proportional to its frequency E photon = h h is Plank’s constant 6.636x Js The intensity (brightness) of radiation is related to the number of photons of a particular frequency

Questions 1.List in order of increasing energy: green light (530 nm), blue light (420 nm), infrared (~10,000 nm). 2.Consider a 1 Watt green laser (532 nm). How many photons are being emitted from the laser per second? 3.Suppose the green laser above is a spot with 1 cm diameter. What is the photon flux in units of W/m 2 ?

Electromagnetic Spectrum Energy increases this way Wavelength increases this way

Solar Emission Flux The sun emits about 6.3 X 10 7 W/m 2 of radiant energy How are we still here?

Radiant Energy Flux Recall FLUX: amount of energy (or mass) passing through an area oriented perpendicular to the flow per unit time. Except for lasers, most objects, such as the sun, radiate in all directions –flux decreases with distance from source. vs r obj d1d1 d2d2 Flux decreases as inverse square of distance from source **this picture is a bit misleading **

Inverse Square Law The reason flux from a “point” source decreases as the inverse square due to the geometry of spheres. The surface area of a sphere is 4  r 2 The further from the initial sphere of radiation, the larger the sphere over which the same total amount of radiation is spread. roro r1r1 r2r2

Spectrum of Solar Radiation Flux “Flux” Shows how the total flux is distributed among different wavelengths. (measured at Earth)

This Week (3) Concepts: Light and Earth’s Energy Balance Electromagnetic Radiation Blackbody Radiation and Temperature Earth’s Energy Balance w/out atmosphere Read chapter 3 (34 – 41.5) of your text Keep up by working on assignment 1

Today—Radiation & Temperature Light and matter The perfect emitter (or absorber) Solar Emission

A Brief Review Yesterday’s key concepts (which will come up again): 1. Light carries energy: E = hv = hc/ 2. The intensity of light is related to the total number of photons (emitted) per time 3. Radiation flux is the amount of light energy passing perpendicularly through a unit area in a second. (J/s/m 2 = W/m 2 ) 4. The radiation flux from a single source decreases by the inverse square of the distance from the source

Oscillators - light - The blue spring is being forced with a frequency it “likes” to oscillate at and thus it absorbs the energy and converts it into vibrational motion

Light and Matter Four possible results of light and matter interaction: 1. Absorption—causes matter to warm 2. Emission – causes matter to cool 3. Transmission – “no interaction” 4. Scattering – like reflection but more general In the end, which of these actually occurs depends on the wavelength (frequency) of light and the type of matter. All processes happen on Earth and are important in considering the energy balance of the planet.

Questions 1.Based on what we’ve learned so far, why would absorption of light cause a temperature increase in some object, and why would emission of light by an object cause a decrease in its temperature? 2.Give a real world example for each of the possible results of light interacting with matter.

Blackbody Radiation A blackbody is a perfect emitter and absorber of radiation. It’s emission spectrum is a function of its temperature only. the peak wavelength... …is inversely proportional to the temperature of the object Hotter objects emit more at shorter wavelengths Radiation Flux (W/m 2 )

Blackbody Radiation A blackbody is a perfect emitter and absorber of radiation. It’s emission spectrum is a function of its temperature only. Radiation Flux (W/m 2 ) Area under curve proportional to total amount of radiation Total amount of radiation emitted is larger for hotter objects.

Blackbody Radiation—So What If I know the emission spectrum of an object, then I know its temperature! (or vice versa) Satellites have used this to measure Earth’s temperature and confirm the increase in T over the past two decades. The hotter an object the more radiation it emits. That is, the more energy it gives off thereby cooling itself faster. This is a negative feedback!

Questions 1.The peak in the sun’s emission spectrum occurs at about 500 nm or 0.5 micrometers. What is the temperature of the sun? 2.How much “brighter” is the sun compared to the Earth?

Imperfect Absorbers/Emitters Kirchoff’s Law: A body can/will only emit the same wavelengths it absorbs. If  (0-1) is the fraction of light absorbed at some wavelength, then only that fraction  (of blackbody radiation) will be emitted at that wavelength. Radiation Flux Distribution Ideal Blackbody distribution True distribution  is known as the emissivity

This Week (3) Concepts: Light and Earth’s Energy Balance Electromagnetic Radiation Blackbody Radiation and Temperature Earth’s Energy Balance w/out atmosphere Read chapter 3 (34 – 41.5) of your text See “Closer Look” on page 42 of your text Keep up by working on assignment 1 (due tomorrow!)

Today—Earth’s Energy Balance Part 1 Setting up the problem (goals and assumptions) How much solar radiation does Earth actually receive? How much of this radiation does Earth absorb? If Energy Flow Rate In = Energy Flow Rate Out, what’s the T?

A Brief Review Yesterday’s key concepts (which will come up again): 1. The total amount of radiant energy emitted by a blackbody is proportional to its T 4 (Stefan-Boltzmann) 2. The hotter the object the more radiation it emits as shorter wavelengths (Wien’s Law) 3. An object which is not a blackbody can be treated as a blackbody as long as its emissivity is known (a result of Kirchoff’s Law)

Solar and Terrestrial Emission Fluxes max ~ 0.5 microns max ~ 10 microns (if they were blackbodies…not so pretty in reality!)

Earth’s Energy Balance To calculate Earth’s equilibrium temperature knowing only: the solar energy flux and how to calculate the terrestrial energy flux to space at a given temperature. Goal Assumptions and Simplifications 1.Energy in = Energy out at all times and locations 2.Solar radiation flux constant in time 3.Everywhere on Earth receives same average solar energy flux 4.Earth is a blackbody (absorbs what it gets w/100% efficiency and thus emits at 100% efficiency)

Earth’s Energy Balance F in = F out What is F in ? Need to account for a) Earth-Sun distance, b) Earth intercepts fraction of total solar flux, and c) Earth “reflects” some of the intercepted radiation D SE RSRS

Earth’s Energy Balance Incoming solar flux at Earth I in = 1370 W/m 2 (solar constant) Earth intercepts an area of this incoming solar radiation equal to a flat disc with R = R earth (Area = pi*R E 2 ) ~ 28% of this intercepted radiation is reflected. This fraction is known as Earth’s albedo. planet I in /4(I in /4)A  T E 4

Earth’s Energy Balance I in (1-A) / 4 =  T E 4 F in = F out This energy balance is good for ANY planet! Though it is always subject to the same assumptions we made.

Earth’s Energy Balance--Summary I in (1-A) / 4 =  T E 4 F in = F out Earth absorbs F IN = 240 W/m 2 of energy (averaged over whole earth surface, day and night) If the earth system radiates like a blackbody then T E = 255 K = -18 C The actual average surface temperature of Earth is about 288 K = 15 C! Where did we mess up???